How do I model a 12 sided shape?
I think there're many ways to model it (e.g. creating one lower segment, arraying it along a curve and using a bridge tool to connect it with circle). I'll show you my solution though :).


Add a cylinder with 12 vertices (change its number in a tool shelf- T). Add a loopcut (Ctrl+R) and place it near the bottom of the cylinder. Then scale the bottom edge a bit. Next select all the horizontal edge loops and subdivide them twice (W-->Subdivide). Select every fourth vertex of the middle edgeloop and place them lower (G,Z). Now select the middle edge loop and press Alt+Shift+S,1. Do the same with the upper one. Finally add the additional edge loops to make the subsurf modifier crease the edges nicely.


Add a subsurf modifier to the cylinder and smooth it. Add two vertical edge loops at the corner of the cylinder, next merge some vertices (Alt+M) and dissolve some edges (X-->Dissolve) as pictured below.


Do it for the other 3 corners. Delete other part of the cylinder and use a mirror modifier to create 3 halfs with the edge loops created.